Optimization Problems

[ayobamiajayi]

im having trouble with these two problems

1. An open box is to be made from a rectangular piece of cardboard, 7 inches by 3 inches, by cutting equal squares from each corner and turning up the sides.

a. write the volume, V, as a function of the edge of the square, x, cut from each corner.

b. use a graphing utility to graph the funtiong V. the nuse the graph of the function to estimate the size of the square that should be cut from each corner and the volume of the largest such box.



2. Use a graphing utility to graph the revenue function R=3x , and the cost function, C = x3 - 6x2 + 10x - 1, where x is given in hundreds of units. (x3 = x cubed)

a. use the graphs to estimate the actual number of units that should be sold to maximize profit.

b. use calculus to determine the actual value of x that maximizes profit



thanks 4 ur help

 

[stapel]

What have you tried? How far have you gotten?

1) You worked with boxes, areas, and volumes back in algebra, so you can at least draw the picture, label lengths and widths, assign variables, etc.

2) You worked with cost, revenue, and profit back in algebra, so you can easily create the "profit" function. Part (a) is plug-n-chug in the calculator, and then looking at the picture. So I'll assume you've got this part done. For part (b), take the derivative of your profit function and see where this leads.

If you get stuck, please reply showing all of your work and reasoning. Thank you!

Eliz.